The source-item coverage of the Lotka function

The following problem has never been studied : Given A, the total number of items (e.g. articles) and T, the total number of sources (e.g. journals that contain these articles) (hence A>T), when is there a Lotka function f(j) = D/j(alpha) that represents this situation (i.e. where to) denotes the density of the sources in the item-density j)? And, if it exists, what are the formulae for D and alpha? This problem is solved in both cases with j is an element of [1, rho]: where (a) rho = infinity and where (b) rho < ∞. Note that p = the maximum density of the items. If ρ = ∞, then A and T determine uniquely D and α. If ρ < infinity, then we have, for every alpha less than or equal to 2, a solution for D and rho, hence for f. If rho < ∞ and α > 2 then we show that a solution exists if and only if mu = A/T < α-1/α-2. This sheds some light on the source-item coverage power of Lotka's law.